Characterizing the community structure of complex networks

Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has been so far devoted to the investigation of communities in real networks. We present a systematic empirical analysis of the statistical properties of communities in large information, communication, technological, biological, and social networks. We find that the mesoscopic organization of networks of the same category is remarkably similar. This is reflected in several characteristics of community structure, which can be used as ``fingerprints'' of specific network categories. While community size distributions are always broad, certain categories of networks consist mainly of tree-like communities, while others have denser modules. Average path lengths within communities initially grow logarithmically with community size, but the growth saturates or slows down for communities larger than a characteristic size. This behaviour is related to the presence of hubs within communities, whose roles differ across categories. Also the community embeddedness of nodes, measured in terms of the fraction of links within their communities, has a characteristic distribution for each category. Our findings are verified by the use of two fundamentally different community detection methods.Comment: 15 pages, 20 figures, 4 table

Identification of important nodes in the information propagation network based on the artificial intelligence method

This study presents an integrated approach for identifying key nodes in information propagation networks using advanced artificial intelligence methods. We introduce a novel technique that combines the Decision-making Trial and Evaluation Laboratory (DEMATEL) method with the Global Structure Model (GSM), creating a synergistic model that effectively captures both local and global influences within a network. This method is applied across various complex networks, such as social, transportation, and communication systems, utilizing the Global Network Influence Dataset (GNID). Our analysis highlights the structural dynamics and resilience of these networks, revealing insights into node connectivity and community formation. The findings demonstrate the effectiveness of our AI-based approach in offering a comprehensive understanding of network behavior, contributing significantly to strategic network analysis and optimization

Hill Climbing-Based Efficient Model for Link Prediction in Undirected Graphs

Link prediction is a key problem in the field of undirected graph, and it can be used in a variety of contexts, including information retrieval and market analysis. By “undirected graphs”, we mean undirected complex networks in this study. The ability to predict new links in complex networks has a significant impact on society. Many complex systems can be modelled using networks. For example, links represent relationships (such as friendships, etc.) in social networks, whereas nodes represent users. Embedding methods, which produce the feature vector of each node in a graph and identify unknown links, are one of the newest approaches to link prediction. The Deep Walk algorithm is a common graph embedding approach that uses pure random walking to capture network structure. In this paper, we propose an efficient model for link prediction based on a hill climbing algorithm. It is used as a cost function. The lower the cost is, the higher the accuracy for link prediction between the source and destination node will be. Unlike other algorithms that predict links based on a single feature, it takes advantage of multiple features. The proposed method has been tested over nine publicly available datasets, and its performance has been evaluated by comparing it to other frequently used indexes. Our model outperforms all of these measures, as indicated by its higher prediction accuracy

Integrating Statistics and Visualization to Improve Exploratory Social Network Analysis

Social network analysis is emerging as a key technique to understanding social, cultural and economic phenomena. However, social network analysis is inherently complex since analysts must understand every individual's attributes as well as relationships between individuals. There are many statistical algorithms which reveal nodes that occupy key social positions and form cohesive social groups. However, it is difficult to find outliers and patterns in strictly quantitative output. In these situations, information visualizations can enable users to make sense of their data, but typical network visualizations are often hard to interpret because of overlapping nodes and tangled edges. My first contribution improves the process of exploratory social network analysis. I have designed and implemented a novel social network analysis tool, SocialAction (http://www.cs.umd.edu/hcil/socialaction) , that integrates both statistics and visualizations to enable users to quickly derive the benefits of both. Statistics are used to detect important individuals, relationships, and clusters. Instead of tabular display of numbers, the results are integrated with a network visualization in which users can easily and dynamically filter nodes and edges. The visualizations simplify the statistical results, facilitating sensemaking and discovery of features such as distributions, patterns, trends, gaps and outliers. The statistics simplify the comprehension of a sometimes chaotic visualization, allowing users to focus on statistically significant nodes and edges. SocialAction was also designed to help analysts explore non-social networks, such as citation, communication, financial and biological networks. My second contribution extends lessons learned from SocialAction and provides designs guidelines for interactive techniques to improve exploratory data analysis. A taxonomy of seven interactive techniques are augmented with computed attributes from statistics and data mining to improve information visualization exploration. Furthermore, systematic yet flexible design goals are provided to help guide domain experts through complex analysis over days, weeks and months. My third contribution demonstrates the effectiveness of long term case studies with domain experts to measure creative activities of information visualization users. Evaluating information visualization tools is problematic because controlled studies may not effectively represent the workflow of analysts. Discoveries occur over weeks and months, and exploratory tasks may be poorly defined. To capture authentic insights, I designed an evaluation methodology that used structured and replicated long-term case studies. The methodology was implemented on unique domain experts that demonstrated the effectiveness of integrating statistics and visualization

Strategic and Stochastic Approaches to Modeling the Structure of Multi-Layer and Interdependent Networks

Examples of complex networks abound in both the natural world (e.g., ecological, social and economic systems), and in engineered applications (e.g., the Internet, the power grid, etc.). The topological structure of such networks plays a fundamental role in their functioning, dictating properties such as the speed of information diffusion, the influence of powerful or vulnerable nodes, and the ability of the nodes to take collective actions. There are two main schools of thought for investigating the structure of complex networks. Early research on this topic primarily adopted a stochastic perspective, postulating that the links between nodes are formed randomly. In an alternative perspective, it has been argued that optimization (rather than pure randomness) plays a key role in network formation. In such settings, edges are formed strategically (either by a designer or by the nodes themselves) in order to maximize certain utility functions. The classical literature on the structure of networks has predominantly focused on single layer networks where there is a single set of edges between nodes. However, there is an increasing realization that many real-world networks have either multi-layer or interdependent structure. While the former considers multiple layers of relationships between the same set of nodes, the latter deals with networks-of-networks consisting of interdependencies between different subnetworks. This thesis focuses on the analysis of the structure of multi-layer and interdependent networks via strategic and stochastic approaches. In the strategic multi-layer network formation setting, each layer represents a different type of relationship between the nodes and is designed to maximize some utility that depends on its own topology and those of the other layers. By viewing the designer of each layer as a player in a multi-layer network formation game, we show that hub-and-spoke networks that are commonly observed in transportation systems arise as a Nash equilibrium. Extending this analysis to interdependent networks where there are different sets of nodes, we introduce a network design game where the objective of the players is to design the interconnections between the nodes of two different networks, G1 and G2. In this game, each player is associated with a node in G1 and has functional dependencies on certain nodes in G2. Besides showing that finding a best response of a player is NP-hard and characterizing some useful properties of the best response actions of the players, we prove existence of pure Nash equilibria in this game under certain conditions. In order to obtain further insights into the structure of interdependent networks with an arbitrary number of subnetworks, we consider a model for random interdependent networks where each edge between two different subnetworks is formed with probability p. We investigate certain spectral and structural properties of such networks, with corresponding implications for certain variants of consensus dynamics on those networks. In particular, we study a property known as r-robustness, which is a strong indicator of the ability of a network, including interdependent networks, to tolerate structural perturbations and dynamical attacks

Complex networks theory for analyzing metabolic networks

One of the main tasks of post-genomic informatics is to systematically investigate all molecules and their interactions within a living cell so as to understand how these molecules and the interactions between them relate to the function of the organism, while networks are appropriate abstract description of all kinds of interactions. In the past few years, great achievement has been made in developing theory of complex networks for revealing the organizing principles that govern the formation and evolution of various complex biological, technological and social networks. This paper reviews the accomplishments in constructing genome-based metabolic networks and describes how the theory of complex networks is applied to analyze metabolic networks.Comment: 13 pages, 2 figure